Folate Receptor Alpha Dendritic Cells (FRαDCs) or Placebo for the Treatment of Patients With Stage III or IV Ovarian, Fallopian Tube, or Primary Peritoneal Cancer, FAROUT Trial

Inclusion Criteria: * Age ≥ 18 years * Histological confirmation of Federation of Gynecology and Obstetrics (FIGO) stage III or stage IV epithelial ovarian, fallopian tube, or primary peritoneal cancer. NOTE: Histologic confirmation of the primary tumor is required. Eligible histotypes include high grade serous; endometrioid; and clear cell carcinoma, as these histotypes have high expression of FRα (Kalli, Oberg, Keeney, \& et al., 2008). Mixed carcinomas, including carcinosarcomas, with ≥ 50% of the tumor comprised of high grade serous; and/or endometrioid; and/or clear cell carcinoma are eligible * Completion of cytoreductive surgery and one (and only one) course of platinum-based chemotherapy (5-9 cycles) ≥ 4 but ≤ 12 weeks prior to registration * NOTE: Cytoreductive surgery may have been prior to or after one or more cycles of chemotherapy and must include hysterectomy and bilateral salpingo-oophorectomy (if the uterus and/or ovaries were not previously removed) * NOTE: Patients may have had more than one chemotherapy regimen (examples: paclitaxel/carboplatin switched to docetaxel/carboplatin due to allergy; or weekly treatment switched to every 3-weekly treatment due to intolerance), but may not have received a separate course of treatment for recurrent OC * NOTE: Patients may receive both neoadjuvant and adjuvant chemotherapy provided both regimens are platinum-based and total nine (9) or fewer chemotherapy cycles * Germline and somatic genetic testing have been completed * NOTE: No pathogenic mutations of BRCA1/BRCA2 are allowed * Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0, 1, or 2 * Expected survival ≥ 6 months * Hemoglobin ≥ 8.5 g/dL (≤ 15 days prior to registration) * Absolute neutrophil count (ANC) ≥ 1000/mm\^3 (≤ 15 days prior to registration) * Platelet count ≥ 75,000/mm\^3 (≤ 15 days prior to registration) * Lymphocytes ≥ 0.3 x 10\^9/L (≤ 15 days prior to registration) * Monocytes ≥ 0.25 x 10\^9/L (≤ 15 days prior to registration) * Total bilirubin ≤ upper limit of normal (ULN), unless patient has a documented history of Gilbert's disease, then direct bilirubin ≤ ULN (≤ 15 days prior to registration) * Aspartate transaminase (AST) ≤ 3 x ULN (≤ 15 days prior to registration) * Creatinine clearance ≥ 30 mL/min per Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) creatinine equation (≤ 15 days prior to registration) * Provide written informed consent * Willing to provide mandatory blood specimens for correlative research * Willing to provide archival tissue specimen for correlative research * Willing to return a participating institution for follow-up (during the active monitoring phase of the study) * Willing to undergo a tetanus vaccination (if not performed ≤ 365 days prior to registration) * Willing to have a central access line placed, if needed (as determined during venous access assessment) Exclusion Criteria: * Any of the following because this study involves an investigational agent, the genotoxic, mutagenic, and teratogenic effects of which on the developing fetus and newborn are unknown * Pregnant persons * Nursing persons * Persons of childbearing potential or able to father a child who are unwilling to employ adequate contraception * Evidence of disease at the time of registration, including clinical concern for disease recurrence based on each of the following: * Evidence of disease by history and physical exam * CA125 outside institutional normal limits * CT (and or MRI) of the chest/abdomen/pelvis demonstrating radiological evidence of disease performed after completion of chemotherapy ≤ 28 days be-fore entering study * Germline or somatic BRCA1 or BRCA2 mutation, as determined by Clinical Laboratory Improvement Act (CLIA)-approved tests * Prior radiation therapy for this cancer * Treatment with chemotherapy, angiogenesis inhibitor therapy, poly (ADP-ribose) polymerase (PARP) inhibitor therapy, radiation therapy, or other immunotherapy ≤ 4 weeks prior to registration * Receiving any other standard therapy (angiogenesis inhibitor, PARP inhibitor) or investigational agent, which would be considered as a treatment for the primary neoplasm. These agents have been shown to be active in later line therapy and can be used at that time for patients who relapse after treatment on this trial * Co-morbid systemic illnesses or other severe concurrent disease which, in the judgment of the investigator, would make the patient inappropriate for entry into this study or interfere significantly with the proper assessment of safety and toxicity of the prescribed regimens * Immunocompromised patients and patients known to be HIV positive and currently receiving antiretroviral therapy * NOTE: Patients known to be HIV positive, but without clinical evidence of an immunocompromised state, are eligible for this trial * Uncontrolled intercurrent illness including, but not limited to: * Ongoing or active infection * Symptomatic congestive heart failure * Unstable angina pectoris * Cardiac arrhythmia * Psychiatric illness/social situations that would limit compliance with study requirements * EXCEPTIONS: HIV-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months are eligible for this trial. For patients with evidence of hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated. Patients with a history of hepatitis C virus (HCV) must have been treated and cured. For patients with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load * Other active malignancy ≤ 3 years prior to registration * EXCEPTIONS: Patients with non-melanotic skin cancer, papillary thyroid cancer not requiring therapy or carcinoma-in-situ are eligible for this trial. Patients with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial. (Contact site principal investigator \[PI\] if questions.) * History of myocardial infarction ≤ 6 months prior to registration, or congestive heart failure requiring use of ongoing maintenance therapy for life-threatening ventricular arrhythmias * NOTE: Patients with known history or current symptoms of cardiac disease, or history of treatment with cardiotoxic agents, should have a clinical risk assessment of cardiac function using the New York Heart Association Functional Classification. To be eligible for this trial, patients should be class 2B or better * Treatment with systemic immunosuppressive medication (including, but not limited to, prednisone, cyclophosphamide, azathioprine, methotrexate, thalidomide, and anti-tumor necrosis factor \[TNF\]-alpha agents) ≤ 2 weeks prior to registration, or anticipation of need for systemic immunosuppressive medication during the course of the study * NOTE: Patients who have received acute, low-dose systemic steroids (≤ 10 mg/day oral prednisone or equivalent) prior to registration or a one-time pulse dose of systemic immunosuppressant medication (e.g., ≤ 48 hours of corticosteroids for a contrast allergy) are eligible for the study * NOTE: The use of inhaled corticosteroids for chronic obstructive pulmonary disease or asthma, mineralocorticoids (e.g., fludrocortisone), or low-dose corticosteroids for patients with orthostatic hypotension or adrenocortical insufficiency is allowed